One must wonder how old you are to have narrowed it down to those two choices. I grew up in the '50s before the family had deteriorated due to "liberal" influences. Families took care of their own to the best of their ability and charities helped out when someone couldn't manage. There are more sane choices than the two you proffer and they don't just spring from a moral and Christian society - they also have the tendency to help expand such a society. Death or the Government is exactly what the Leftist Commies want the People to think of as the two alternatives.
Given many families are in economic trouble, I failed to consider the family as the caretaker. Of course if at all possible YES the family is the lead responsibility. Government support follows if there’s no family to support a disabled person and of course it depend on the degree of support which a disabled person needs.